Spectral analysis and long-time asymptotics of complex mKdV equation

In this paper, we obtain the long-time asymptotics of complex mKdV equation via Defit-Zhou method (Non-linear steepest descent method). The Cauchy problem is transformed into corresponding Riemann-Hilbert on basis Lax pair and scattering matrix. After that problems are converted through a decomposition matrix-valued spectral function factorizations jump matrix for problem. Finally, by solving last model problem, derived.